In hadronic collisions, interference between different production channels affects momentum distributions of multi-particle final states. As this QCD interference does not depend on the strong coupling constant αs, it is part of the no-interaction baseline that needs to be controlled prior to searching for other manifestations of collective dynamics, e.g., in the analysis of azimuthal anisostropy coefficients vn at the LHC. Here, we introduce a model that is based on the QCD theory of multi-parton interactions and that allows one to study interference effects in the production of m particles in hadronic collisions with N parton-parton interactions (“sources”). In an expansion in powers of 1/(Nc2 − 1) and to leading order in the number of sources N , we calculate interference effects in the m-particle spectra and we determine from them the second and fourth order cumulant momentum anisotropies vn{2} and vn{4}. Without invoking any azimuthal asymmetry and any density dependent non-linear dynamics in the incoming state, and without invoking any interaction in the final state, we find that QCD interference alone can give rise to values for vn{2} and vn{4}, n even, that persist unattenuated for increasing number of sources, that may increase with increasing multiplicity and that agree with measurements in proton-proton (pp) collisions in terms of the order of magnitude of the signal and the approximate shape of the transverse momentum dependence. We further find that the non-abelian features of QCD interference can give rise to odd harmonic anisotropies. These findings indicate that the no-interaction baseline including QCD interference effects can make a sizeable if not dominant contribution to the measured vn coefficients in pp collisions. Prospects for analyzing QCD interference contributions further and their possible relevance for proton-nucleus and nucleus-nucleus collisions are discussed shortly.